so correct to four decimal places.
EXAMPLE 52
Estimate the error if the approximate formula
is used and |x| < 0.02.
SOLUTION: We obtain the first few terms of the Maclaurin series generated by
Then
Note that for x < 0, the series is not alternating, so we must use the Lagrange error bound. Here
where −0.02 < c < 0.02. With |x| < 0.02, we see that the upper bound uses c = −0.02:
EXAMPLE 53
Use a series to evaluate
SOLUTION: From series (1) in Common Maclaurin Series,
Then
a well-established result obtained previously.
EXAMPLE 54
Use a series to evaluate
SOLUTION: We can use series (4) in Common Maclaurin Series, and write